A pyramid would seem to fit the given description.
Pyramid
A geometric figure with a polygonal base and triangular sides is called a pyramid.
A polygonal pyramid.
pyramid
pyramid
All but one face must be triangular. The base can be any polygon, including a triangle.
a polygonal prism or a polygond
A pyramid.
A pyramid.
The description given fits to that of a pyramid
A cylinder is a polygon that has circles as its base. A triangular pyramid is a polygon that has a triangle as its base.
If I am correct I'm sure any pyramid does now if you knew what shape the base is or how many triangle faces I could answer